Breed family: Difference between revisions

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The '''breed family''' of [[rank-3 ~~temperament|rank-3]] [[regular temperament|~~temperament]]s are [[microtemperament]]s which [[tempering out|temper out]] [[2401/2400]].

The '''breed family''' of [[rank-3 temperament]]s are [[microtemperament]]s which [[tempering out|temper out]] [[2401/2400]].

== Breed ==

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Jove (formerly known as wonder) tempers out [[243/242]], [[441/440]], and [[540/539]]. Jove converts breed into an 11-limit temperament via 441/440, which equates [[49/40]] with [[11/9]], and 243/242, which tells us 11/9 can serve as a neutral third. While jove is no longer a super-accurate microtemperament like breed, it has the advantage of adjusting its tuning to deal with the 11-limit. [[72edo|72]], [[130edo|130]], [[171edo|171]] and [[202edo|202]] are good edo tunings for jove.

Jove (formerly known as wonder) tempers out [[243/242]], [[441/440]], and [[540/539]]. Jove converts breed into an 11-limit temperament via 441/440, which equates [[49/40]] with [[11/9]], and 243/242, which tells us 11/9 can serve as a neutral third (as in exactly half of [[~]][[3/2]]). While jove is no longer a super-accurate microtemperament like breed, it has the advantage of adjusting its tuning to deal with the 11-limit. [[72edo|72]], [[130edo|130]], [[171edo|171]] and [[202edo|202]] are good edo tunings for jove.

[[Subgroup]]: 2.3.5.7.11

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Badness (Sintel): 2.29

=== Jovis ===

Subgroup: 2.3.5.7.11.13

Comma list: 243/242, 351/350, 441/440

Mapping: {{mapping| 1 1 1 2 2 2 | 0 2 1 1 5 -3 | 0 0 2 1 0 5 }}

Optimal tunings:

* WE: ~2 = 1200.1435{{c}}, ~11/9 = 350.4354{{c}}, ~10/7 = 618.1775{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 350.4402{{c}}, ~10/7 = 618.1759{{c}}

{{Optimal ET sequence|legend=0| 27e, 31, 45ef, 58, 72, 103, 130, 233, 363 }}

Badness (Sintel): 0.507

=== Jofur ===

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Badness (Sintel): 0.701

=== ~~Jovis~~ ===

=== Semijove ===

Subgroup: 2.3.5.7.11.13

Comma list: 243/242, ~~351~~/~~350~~, ~~441~~/~~440~~

Comma list: 243/242, 441/440, 676/675

Mapping: {{mapping| 1 1 1 ~~2 2 2~~ | 0 2 1 1 5 -3 | 0 0 2 1 0 5 }}

Mapping: {{mapping| 2 0 1 3 -1 -1 | 0 2 1 1 5 4 | 0 0 2 1 0 2 }}

: mapping generators: ~55/39, ~26/15, ~10/7

Optimal tunings:

* WE: ~2 = ~~1200~~.~~1435~~{{c}}, ~11/9 = ~~350~~.~~4354~~{{c}}, ~10/7 = 618.~~1775~~{{c}}

* WE: ~55/39 = 599.9886{{c}}, ~26/15 = 950.6645{{c}}, ~10/7 = 618.1458{{c}}

* CWE: ~2 = ~~1200~~.0000{{c}}, ~11/9 = ~~350~~.~~4402~~{{c}}, ~10/7 = 618.~~1759~~{{c}}

* CWE: ~55/39 = 600.0000{{c}}, ~26/15 = 950.6755{{c}}, ~10/7 = 618.1489{{c}}

{{Optimal ET sequence|legend=0| ~~27e, 31, 45ef~~, 58, 72~~, 103~~, 130~~, 233, 363~~ }}

Badness (Sintel): 0.~~507~~

Badness (Sintel): 0.948

== Agni ==

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== Lif ==

Lif tempers out the [[olympia]] and readily extends to the [[13-limit]] and the no-17 [[19-limit]] ~~such that~~ the ~~undevicesimal schisma of~~ [[513/512]] is equated with ~~[[441/440]][[~]][[540/539]]~~.

Lif tempers out the [[olympia]] and the [[lifthrasirsma]], so that the [[rastma]] is split in halves with each part standing in not only for [[441/440]][[~]][[540/539]], but the [[32805/32768|schisma]]. Lif readily extends to the [[13-limit]] and the no-17 [[19-limit]], where the [[513/512|undevicesimal schisma]] is also equated with the schisma.

This temperament was named by [[Flora Canou]] in 2023 along with the [[weak restriction]], [[lifthrasir]], and the corresponding comma [[lifthrasirsma]], after the human survivors of Ragnarök.

This temperament was named by [[Flora Canou]] in 2023 along with the [[weak restriction]], [[lifthrasir]], and the corresponding comma, lifthrasirsma, after the human survivors of Ragnarök.

[[Subgroup]]: 2.3.5.7.11

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[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.9386{{c}}, ~49/40 = ~~350~~.0586{{c}}, ~10/7 = 617.7065{{c}}

* [[WE]]: ~2 = 1199.9386{{c}}, ~49/40 = 351.0586{{c}}, ~10/7 = 617.7065{{c}}

: [[error map]]: {{val| -0.061 +0.101 +0.096 -0.184 +0.075 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 351.0806{{c}}, ~10/7 = 617.7228{{c}}

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Badness (Sintel): 0.488

== Freyr ==

Freyr tempers out the [[symbiotic comma]], so that the [[rastma]] is split in halves with each part standing in not only for [[441/440]][[~]][[540/539]], but the [[5120/5103|aberschisma]]. Freyr easily extends to the [[13-limit]], equating the [[352/351|major minthma]] with the aberschisma, and the no-17 [[19-limit]], equating the [[513/512|undevicesimal schisma]] with it too.

It can be notated with [[neutral chain-of-fifths notation]] with two additional sets of accidentals, one for the generic comma step, and the other for the generic aberschisma step.

This temperament was named by [[Flora Canou]] in 2026, under the impression that it functions as a counterpart of [[#Freya|freya]].

[[Subgroup]]: 2.3.5.7.11

[[Comma list]]: 2401/2400, 19712/19683

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.9474{{c}}, ~49/40 = 351.1064{{c}}, ~10/7 = 617.6483{{c}}

: [[error map]]: {{val| -0.053 +0.205 +0.037 -0.176 -0.104 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 351.1156{{c}}, ~10/7 = 617.6499{{c}}

: error map: {{val| 0.000 +0.276 +0.102 -0.060 -0.003 }}

{{Optimal ET sequence|legend=1| 41, 58, 99e, 171e, 212, 270, 581, 851, 1121, 1972, 2881bc }}

[[Badness]] (Sintel): 1.23

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 2401/2400, 10648/10647

Mapping: {{mapping| 1 1 1 2 -1 -2 | 0 2 1 1 17 23 | 0 0 2 1 -1 -2 }}

Optimal tunings:

* WE: ~2 = 1199.9432{{c}}, ~49/40 = 351.1128{{c}}, ~10/7 = 617.6419{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.1232{{c}}, ~10/7 = 617.6431{{c}}

{{Optimal ET sequence|legend=0| 41, 58, 99ef, 154cef, 171ef, 212, 270, 581, 851, 1490, 1760, 2071be, 2341b }}

Badness (Sintel): 0.760

=== 2.3.5.7.11.13.19 subgroup ===

Subgroup: 2.3.5.7.11.13.19

Comma list: 1216/1215, 1540/1539, 2080/2079, 2401/2400

Mapping: {{mapping| 1 1 1 2 -1 -2 0 | 0 2 1 1 17 23 11 | 0 0 2 1 -1 -2 2 }}

Optimal tunings:

* WE: ~2 = 1199.9435{{c}}, ~49/40 = 351.1127{{c}}, ~10/7 = 617.6404{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.1236{{c}}, ~10/7 = 617.6459{{c}}

{{Optimal ET sequence|legend=0| 41, 58h, 99ef, 171ef, 212h, 270, 581, 851, 1490h, 1760h, 2071beh, 2341bh }}

Badness (Sintel): 0.523

== Baldur ==

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== Freya ==

Freya tempers out [[3025/3024]] and [[41503/41472]], so it splits breed's [[28/27]] into two [[55/54]]~[[56/55]]'s and [[8/7]] into two [[77/72]]'s. It also takes the [[225/224]][[~]][[1029/1024]] [[kleisma #As an interval region|kleisma]] to represent [[243/242]], and splits it in half to get [[385/384]], [[441/440]], and [[540/539]]. Since these are the commas tempered out by [[miracle]], the simple relations between them make freya an elegant miracle detemperament.

[[Subgroup]]: 2.3.5.7.11

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[[Badness]] (Sintel): 0.204

[[Projection pair]]s: ~3 ~~= ~~~2401/800, ~5 ~~= ~~~22880495169/4575312500, ~7 ~~= ~~~1058841/151250, ~11 ~~= ~~~33275/3024 to 2.49/5.77/3

[[Projection pair]]s: <code>3 2401/800, 5 22880495169/4575312500, 7 1058841/151250, 11 33275/3024</code> to 2.49/5.77/3

=== 13-limit ===

Freya's canonical 13-limit extension maps [[352/351]] to the half-kleisma. It has [[miraculous]] as a sub-temperament.

Subgroup: 2.3.5.7.11.13

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=== Eir ===

[[User:VIxen|VIxen]] named this extension after a healer goddess or valkyrie from the Norse mythology, as it is an extension of freya with the ibnsinma that evokes associations with medicine.

[[User:VIxen|VIxen]] named this extension after a healer goddess or valkyrie from the Norse mythology, as it is an extension of freya with the [[ibnsinma]] that evokes associations with medicine. It maps [[325/324]], [[364/363]], and [[729/728]] to the half-kleisma and has [[manna]] as a sub-temperament.

Subgroup: 2.3.5.7.11.13

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=== Heimlaug ===

VIxen named this extension after a völva (seeress) from the Gull-Þóris saga of Icelanders. It is an extension of freya with the [[1001/1000|fairytale comma]] and the [[936/935|ainisma]], both adding to the mystical theme. The one of prophecy is bolstered by that this extension has [[benediction]] as a subtemperament.

VIxen named this extension after a völva (seeress) from the Gull-Þóris saga of Icelanders. It is an extension of freya with the [[1001/1000|fairytale comma]] and the [[936/935|ainisma]], both adding to the mystical theme. The one of prophecy is bolstered by that this extension has [[benediction]] as a subtemperament. It maps [[351/350]] and [[625/624]] to the half-kleisma.

Subgroup: 2.3.5.7.11.13

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==== 17-limit ====

~~Equave 10/7 and 16-note scales with that period are of interest.~~

Subgroup: 2.3.5.7.11.13.17

Comma list: 715/714, 936/935, 1001/1000, 1225/1224~~, 1716/1715~~

Comma list: 715/714, 936/935, 1001/1000, 1225/1224

Mapping: {{mapping| 1 1 -1 1 5 -6 -5 | 0 2 3 2 1 6 6 | 0 0 4 2 -3 13 12 }}

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* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 350.9526{{c}}, ~70/39 = 1013.3747{{c}}

{{Optimal ET sequence|legend=0| 45ef, 58, 103, 161, 212, 270, 643, 913f, 1614ef }} ~~<nowiki>~~*~~</nowiki>~~

{{Optimal ET sequence|legend=0| 45ef, 58, 103, 161, 212, 270, 643, 913f, 1614ef }} *

<nowiki>*~~</nowiki> [[~~optimal patent val]]: [[1241edo|1241]]

<nowiki/>* optimal patent val: [[1241edo|1241]]

Badness (Sintel): 0.873

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: error map: {{val| 0.000 +0.021 -0.016 -0.183 -0.040 }}

{{Optimal ET sequence|legend=1| 72~~, …~~, 171, 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 6561dd, 6903dd }}

{{Optimal ET sequence|legend=1| 72, 171(e), 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 6561dd, 6903dd }}

[[Badness]] (Sintel): 0.330

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* CWE: ~27/25 = 133.3333{{c}}, ~5/3 = 884.3905{{c}}, ~11/8 = 551.7085{{c}}

{{Optimal ET sequence|legend=0| 72~~, …~~, 171, 198, 270, 639, 711, 981, 1692e }}

{{Optimal ET sequence|legend=0| 72, 171(ef), 198, 270, 639, 711, 981, 1692e }}

Badness (Sintel): 0.706

[[Category:Breed family| ]]

[[Category:Temperament families]]

[[Category:~~Breed family| ]] <!~~-~~- main article -->~~

[[Category:Catalogs of rank-3 temperaments]]

~~[[Category:Rank~~ 3]]

@@ Line 1: / Line 1: @@
 {{Technical data page}}
-The '''breed family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperament]]s are [[microtemperament]]s which [[tempering out|temper out]] [[2401/2400]].
+The '''breed family''' of [[rank-3 temperament]]s are [[microtemperament]]s which [[tempering out|temper out]] [[2401/2400]].
 == Breed ==
@@ Line 41: / Line 41: @@
 {{Main| Jove }}
-Jove (formerly known as wonder) tempers out [[243/242]], [[441/440]], and [[540/539]]. Jove converts breed into an 11-limit temperament via 441/440, which equates [[49/40]] with [[11/9]], and 243/242, which tells us 11/9 can serve as a neutral third. While jove is no longer a super-accurate microtemperament like breed, it has the advantage of adjusting its tuning to deal with the 11-limit. [[72edo|72]], [[130edo|130]], [[171edo|171]] and [[202edo|202]] are good edo tunings for jove.
+Jove (formerly known as wonder) tempers out [[243/242]], [[441/440]], and [[540/539]]. Jove converts breed into an 11-limit temperament via 441/440, which equates [[49/40]] with [[11/9]], and 243/242, which tells us 11/9 can serve as a neutral third (as in exactly half of [[~]][[3/2]]). While jove is no longer a super-accurate microtemperament like breed, it has the advantage of adjusting its tuning to deal with the 11-limit. [[72edo|72]], [[130edo|130]], [[171edo|171]] and [[202edo|202]] are good edo tunings for jove.
 [[Subgroup]]: 2.3.5.7.11
@@ Line 131: / Line 131: @@
 Badness (Sintel): 2.29
+=== Jovis ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 243/242, 351/350, 441/440
+Mapping: {{mapping| 1 1 1 2 2 2 | 0 2 1 1 5 -3 | 0 0 2 1 0 5 }}
+Optimal tunings:
+* WE: ~2 = 1200.1435{{c}}, ~11/9 = 350.4354{{c}}, ~10/7 = 618.1775{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 350.4402{{c}}, ~10/7 = 618.1759{{c}}
+{{Optimal ET sequence|legend=0| 27e, 31, 45ef, 58, 72, 103, 130, 233, 363 }}
+Badness (Sintel): 0.507
 === Jofur ===
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 Badness (Sintel): 0.701
-=== Jovis ===
+=== Semijove ===
 Subgroup: 2.3.5.7.11.13
-Comma list: 243/242, 351/350, 441/440
+Comma list: 243/242, 441/440, 676/675
-Mapping: {{mapping| 1 1 1 2 2 2 | 0 2 1 1 5 -3 | 0 0 2 1 0 5 }}
+Mapping: {{mapping| 2 0 1 3 -1 -1 | 0 2 1 1 5 4 | 0 0 2 1 0 2 }}
+: mapping generators: ~55/39, ~26/15, ~10/7
 Optimal tunings:
-* WE: ~2 = 1200.1435{{c}}, ~11/9 = 350.4354{{c}}, ~10/7 = 618.1775{{c}}
+* WE: ~55/39 = 599.9886{{c}}, ~26/15 = 950.6645{{c}}, ~10/7 = 618.1458{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 350.4402{{c}}, ~10/7 = 618.1759{{c}}
+* CWE: ~55/39 = 600.0000{{c}}, ~26/15 = 950.6755{{c}}, ~10/7 = 618.1489{{c}}
-{{Optimal ET sequence|legend=0| 27e, 31, 45ef, 58, 72, 103, 130, 233, 363 }}
+{{Optimal ET sequence|legend=0| 48c, 58, 72, 130 }}
-Badness (Sintel): 0.507
+Badness (Sintel): 0.948
 == Agni ==
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 == Lif ==
-Lif tempers out the [[olympia]] and readily extends to the [[13-limit]] and the no-17 [[19-limit]] such that the undevicesimal schisma of [[513/512]] is equated with [[441/440]][[~]][[540/539]].
+Lif tempers out the [[olympia]] and the [[lifthrasirsma]], so that the [[rastma]] is split in halves with each part standing in not only for [[441/440]][[~]][[540/539]], but the [[32805/32768|schisma]]. Lif readily extends to the [[13-limit]] and the no-17 [[19-limit]], where the [[513/512|undevicesimal schisma]] is also equated with the schisma.
-This temperament was named by [[Flora Canou]] in 2023 along with the [[weak restriction]], [[lifthrasir]], and the corresponding comma [[lifthrasirsma]], after the human survivors of Ragnarök.
+This temperament was named by [[Flora Canou]] in 2023 along with the [[weak restriction]], [[lifthrasir]], and the corresponding comma, lifthrasirsma, after the human survivors of Ragnarök.
 [[Subgroup]]: 2.3.5.7.11
@@ Line 249: / Line 265: @@
 [[Optimal tuning]]s:
-* [[WE]]: ~2 = 1199.9386{{c}}, ~49/40 = 350.0586{{c}}, ~10/7 = 617.7065{{c}}
+* [[WE]]: ~2 = 1199.9386{{c}}, ~49/40 = 351.0586{{c}}, ~10/7 = 617.7065{{c}}
 : [[error map]]: {{val| -0.061 +0.101 +0.096 -0.184 +0.075 }}
 * [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 351.0806{{c}}, ~10/7 = 617.7228{{c}}
@@ Line 287: / Line 303: @@
 Badness (Sintel): 0.488
+== Freyr ==
+Freyr tempers out the [[symbiotic comma]], so that the [[rastma]] is split in halves with each part standing in not only for [[441/440]][[~]][[540/539]], but the [[5120/5103|aberschisma]]. Freyr easily extends to the [[13-limit]], equating the [[352/351|major minthma]] with the aberschisma, and the no-17 [[19-limit]], equating the [[513/512|undevicesimal schisma]] with it too.
+It can be notated with [[neutral chain-of-fifths notation]] with two additional sets of accidentals, one for the generic comma step, and the other for the generic aberschisma step.
+This temperament was named by [[Flora Canou]] in 2026, under the impression that it functions as a counterpart of [[#Freya|freya]].
+[[Subgroup]]: 2.3.5.7.11
+[[Comma list]]: 2401/2400, 19712/19683
+{{Mapping|legend=1| 1 1 1 2 -1 | 0 2 1 1 17 | 0 0 2 1 -1 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9474{{c}}, ~49/40 = 351.1064{{c}}, ~10/7 = 617.6483{{c}}
+: [[error map]]: {{val| -0.053 +0.205 +0.037 -0.176 -0.104 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 351.1156{{c}}, ~10/7 = 617.6499{{c}}
+: error map: {{val| 0.000 +0.276 +0.102 -0.060 -0.003 }}
+{{Optimal ET sequence|legend=1| 41, 58, 99e, 171e, 212, 270, 581, 851, 1121, 1972, 2881bc }}
+[[Badness]] (Sintel): 1.23
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 2080/2079, 2401/2400, 10648/10647
+Mapping: {{mapping| 1 1 1 2 -1 -2 | 0 2 1 1 17 23 | 0 0 2 1 -1 -2 }}
+Optimal tunings:
+* WE: ~2 = 1199.9432{{c}}, ~49/40 = 351.1128{{c}}, ~10/7 = 617.6419{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.1232{{c}}, ~10/7 = 617.6431{{c}}
+{{Optimal ET sequence|legend=0| 41, 58, 99ef, 154cef, 171ef, 212, 270, 581, 851, 1490, 1760, 2071be, 2341b }}
+Badness (Sintel): 0.760
+=== 2.3.5.7.11.13.19 subgroup ===
+Subgroup: 2.3.5.7.11.13.19
+Comma list: 1216/1215, 1540/1539, 2080/2079, 2401/2400
+Mapping: {{mapping| 1 1 1 2 -1 -2 0 | 0 2 1 1 17 23 11 | 0 0 2 1 -1 -2 2 }}
+Optimal tunings:
+* WE: ~2 = 1199.9435{{c}}, ~49/40 = 351.1127{{c}}, ~10/7 = 617.6404{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.1236{{c}}, ~10/7 = 617.6459{{c}}
+{{Optimal ET sequence|legend=0| 41, 58h, 99ef, 171ef, 212h, 270, 581, 851, 1490h, 1760h, 2071beh, 2341bh }}
+Badness (Sintel): 0.523
 == Baldur ==
@@ Line 348: / Line 417: @@
 == Freya ==
+Freya tempers out [[3025/3024]] and [[41503/41472]], so it splits breed's [[28/27]] into two [[55/54]]~[[56/55]]'s and [[8/7]] into two [[77/72]]'s. It also takes the [[225/224]][[~]][[1029/1024]] [[kleisma #As an interval region|kleisma]] to represent [[243/242]], and splits it in half to get [[385/384]], [[441/440]], and [[540/539]]. Since these are the commas tempered out by [[miracle]], the simple relations between them make freya an elegant miracle detemperament.
 [[Subgroup]]: 2.3.5.7.11
@@ Line 368: / Line 439: @@
 [[Badness]] (Sintel): 0.204
-[[Projection pair]]s: ~3 = ~2401/800, ~5 = ~22880495169/4575312500, ~7 = ~1058841/151250, ~11 = ~33275/3024 to 2.49/5.77/3
+[[Projection pair]]s: <code>3 2401/800, 5 22880495169/4575312500, 7 1058841/151250, 11 33275/3024</code> to 2.49/5.77/3
 === 13-limit ===
+Freya's canonical 13-limit extension maps [[352/351]] to the half-kleisma. It has [[miraculous]] as a sub-temperament.
 Subgroup: 2.3.5.7.11.13
@@ Line 388: / Line 461: @@
 === Eir ===
-[[User:VIxen|VIxen]] named this extension after a healer goddess or valkyrie from the Norse mythology, as it is an extension of freya with the ibnsinma that evokes associations with medicine.
+[[User:VIxen|VIxen]] named this extension after a healer goddess or valkyrie from the Norse mythology, as it is an extension of freya with the [[ibnsinma]] that evokes associations with medicine. It maps [[325/324]], [[364/363]], and [[729/728]] to the half-kleisma and has [[manna]] as a sub-temperament.
 Subgroup: 2.3.5.7.11.13
@@ Line 435: / Line 508: @@
 === Heimlaug ===
-VIxen named this extension after a völva (seeress) from the Gull-Þóris saga of Icelanders. It is an extension of freya with the [[1001/1000|fairytale comma]] and the [[936/935|ainisma]], both adding to the mystical theme. The one of prophecy is bolstered by that this extension has [[benediction]] as a subtemperament.
+VIxen named this extension after a völva (seeress) from the Gull-Þóris saga of Icelanders. It is an extension of freya with the [[1001/1000|fairytale comma]] and the [[936/935|ainisma]], both adding to the mystical theme. The one of prophecy is bolstered by that this extension has [[benediction]] as a subtemperament. It maps [[351/350]] and [[625/624]] to the half-kleisma.
 Subgroup: 2.3.5.7.11.13
@@ Line 452: / Line 525: @@
 ==== 17-limit ====
-Equave 10/7 and 16-note scales with that period are of interest.
 Subgroup: 2.3.5.7.11.13.17
-Comma list: 715/714, 936/935, 1001/1000, 1225/1224, 1716/1715
+Comma list: 715/714, 936/935, 1001/1000, 1225/1224
 Mapping: {{mapping| 1 1 -1 1 5 -6 -5 | 0 2 3 2 1 6 6 | 0 0 4 2 -3 13 12 }}
@@ Line 530: / Line 601: @@
 * CWE: ~2 = 1200.0000{{c}}, ~49/40 = 350.9526{{c}}, ~70/39 = 1013.3747{{c}}
-{{Optimal ET sequence|legend=0| 45ef, 58, 103, 161, 212, 270, 643, 913f, 1614ef }} <nowiki>*</nowiki>
+{{Optimal ET sequence|legend=0| 45ef, 58, 103, 161, 212, 270, 643, 913f, 1614ef }} *
-<nowiki>*</nowiki> [[optimal patent val]]: [[1241edo|1241]]
+<nowiki/>* optimal patent val: [[1241edo|1241]]
 Badness (Sintel): 0.873
@@ Line 551: / Line 623: @@
 : error map: {{val| 0.000 +0.021 -0.016 -0.183 -0.040 }}
-{{Optimal ET sequence|legend=1| 72, …, 171, 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 6561dd, 6903dd }}
+{{Optimal ET sequence|legend=1| 72, 171(e), 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 6561dd, 6903dd }}
 [[Badness]] (Sintel): 0.330
@@ Line 566: / Line 638: @@
 * CWE: ~27/25 = 133.3333{{c}}, ~5/3 = 884.3905{{c}}, ~11/8 = 551.7085{{c}}
-{{Optimal ET sequence|legend=0| 72, …, 171, 198, 270, 639, 711, 981, 1692e }}
+{{Optimal ET sequence|legend=0| 72, 171(ef), 198, 270, 639, 711, 981, 1692e }}
 Badness (Sintel): 0.706
+[[Category:Breed family| ]] <!-- main article -->
 [[Category:Temperament families]]
-[[Category:Breed family| ]] <!-- main article -->
+[[Category:Catalogs of rank-3 temperaments]]
-[[Category:Rank 3]]